In fluid dynamics, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given volume per unit time (for example gallons per minute or squeaks per parsec). It is also called flux. It is usually represented by the symbol Q. Fluid dynamics is the subdiscipline of fluid mechanics that studies fluids (liquids and gases) in motion. ... In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks. ...

Given an area A, and a fluid flowing through it with uniform velocity v with an angle θ away from the perpendicular to A, the flux is: Area is a physical quantity expressing the size of a part of a surface. ... The velocity of an object is simply its speed in a particular direction. ... Perpendicular is a geometric term that may be used as a noun or adjective. ...

In the special case where the flow is perpendicular to the area A, that is, θ = 0, the flux is:

If the velocity of the fluid through the area is non-uniform (or if the area is non-planar) then the rate of fluid flow can be calculated by means of a surface integral: In mathematics, a surface integral is a definite integral taken over some surface that may be a curved set in space; it can be thought of as the double integral analog of the path integral. ...

where dS is a differential surface described by:

with n the unit surface normal and dA the differential magnitude of the area. A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ...

If a surface S encloses a volume V, the divergence theorem states that the rate of fluid flow through the surface is the integral of the divergence of the velocity vector field v on that volume: In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky–Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ... In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ...

See also

• Discharge (hydrology)
• Flowmeter
• Mass flow rate
• Orifice plate
• Monkey Orifices